Let \(Y_i=\frac{1}{n}\sum _{i=1}^n \frac{X_i-T_P(P)}{\Vert X_i-T_P(P)\Vert }\psi _P(\Vert X_i-T_P(P)\Vert )\)  for \(1\le i\le d\) , from [1]}, there exists an absolute constant \(K>0\)  such that
\(\mathbb {E}\left[\left\Vert \sum _{i=1} ^n Y_i \right\Vert ^{pq}\right]^{1/(pq)}\le Kpq\left(\mathbb {E}\left[\left\Vert \sum _{i=1} ^n Y_i \right\Vert ^{2}\right]^{1/2}+\mathbb {E}\left[\max _{1\le i\le n}\left\Vert  Y_i \right\Vert ^{pq}\right]^{1/(pq)} \right).\) 
